what is complex number
DESCRIPTION
Its a brief note on complex numbers.TRANSCRIPT
![Page 1: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/1.jpg)
1(Complex Number)
![Page 2: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/2.jpg)
(Complex Number) 2
Presented by:Hamza Sajjad
![Page 3: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/3.jpg)
History.
Number System.
Complex numbers.
Operations.
3(Complex Number)
![Page 4: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/4.jpg)
Complex numbers were first introduced by G. Cardano
R. Bombelli introduced the symbol 𝑖.
A. Girard called “solutions impossible”.
C. F. Gauss called “complex number”
4(Complex Number)
![Page 5: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/5.jpg)
5(Complex Number)
Real Number
Irrational Number
Rational Number
Natural Number
Whole Number
Integer
Imaginary Numbers
![Page 6: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/6.jpg)
When we combine the real and imaginary number then complex number is form.
6(Complex Number)
Real Number
Imaginary Number
Complex Number
![Page 7: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/7.jpg)
7(Complex Number)
• A complex number is a number that can b express in the form of "a+b𝒊".
• Where a and b are real number and 𝑖 is an imaginary.
• In this expression, a is the real part and b is the imaginary part of complex number.
![Page 8: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/8.jpg)
8(Complex Number)
• A complex number has a real part and an imaginary part, But either part can be 0 .
• So, all real number and Imaginary number are also complex number.
![Page 9: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/9.jpg)
9(Complex Number)
Complex number extend the concept of one-dimensional number line to the two-dimensional complex plan.
![Page 10: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/10.jpg)
10(Complex Number)
• Horizontal axis use for real part. • Vertical axis for the imaginary part.
![Page 11: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/11.jpg)
11(Complex Number)
Complex number convert our visualization into physical things.
![Page 12: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/12.jpg)
12(Complex Number)
Addition :Complex number added by adding real part in real
and imaginary part in imaginary.
(a + b𝑖) + (c + d 𝑖) = (a + c) + (b + d) 𝑖.
Subtraction:Similarly, subtraction is defined
(a + b𝑖) - (c + d 𝑖 ) = (a - c) + (b - d) 𝑖 .
![Page 13: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/13.jpg)
13(Complex Number)
Multiplication:
The multiplication of two complex number is define by the following formula:
(a + b𝑖).(c + d 𝑖 ) =(ac - bd) + (b c + ad) 𝑖Square of the imaginary unit is -1.
𝑖²=𝑖 ∗ 𝑖= -1
Division:Division can be defined as:
𝑎 + 𝑏𝑖
𝑐 + 𝑑𝑖= (
𝑎𝑐+𝑏𝑑
𝑐²+𝑑²) (
𝑏𝑐−𝑎𝑑
𝑐²+𝑑²)𝑖+
![Page 14: What is complex number](https://reader033.vdocuments.us/reader033/viewer/2022052508/559e9f551a28abe5048b47c9/html5/thumbnails/14.jpg)
14(Complex Number)